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Graphing Quadratic Functions and Finding Vertex

Learn how to graph quadratic functions, identify their vertex and axis of symmetry, and find maximum or minimum values. Practice problems included.

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Graphing Quadratic Functions and Finding Vertex

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  1. Do Now • Find the value of y when x = -1, 0, and 2. • y = x2 + 3x – 2 • y = 2x2 + 2x – 24 • y = -x2 + 2x + 2

  2. 2.2: Characteristics of Quadratic Functions Objective: graph quadratic functions and identify their vertex and axis of symmetry

  3. Axis of symmetry • The axis of symmetry is a line that divides a parabola into mirror images and passes through the vertex. • Cuts a parabola in half

  4. Example 1: • Plot the vertex at (- 3, 4). • The axis of symmetry will be at the line vertically along the x value of the vertex. • x = -3 • Plot two more points on the graph • (- 2, 2) and (- 1, - 4) • Draw the parabola through the points.

  5. Practice • Graph y = 3(x - 2)2+ 1. Label the vertex and axis of symmetry.

  6. Quadratic Functions

  7. Quadratic Equation • Standard Form: f(x) = ax2 + bx + c • Equation for the line of symmetry: • x-coordinate of vertex (find y-value by plugging in x-value and solving):

  8. Steps to graphing a quadratic equation in standard form: Standard form: f(x) = ax2 + bx + c 1.) Find x-coordinate of the vertex: 2.) Create table with x-coordinate of vertex in the middle and choose at least one value smaller than vertex and one value larger than vertex for x. 3.) Plug in values for x and solve for y. 4.) Plot points and draw parabola.

  9. Graph f(x) = -4x2 + 8x+ 2

  10. Quadratic Equation

  11. Graphing using intercept form f(x) = a(x – p)(x – q) • Plot the x-intercepts: points p and q • Find x-coordinate of vertex by averagingp and q: • Find y-coordinate of vertex by plugging in x-coordinate and solving. Plot the vertex.

  12. Graph f(x) = (x + 2)(x – 2)

  13. Graph y = 3(x + 3)(x + 5)

  14. Finding Maximum and Minimum Values

  15. Find the Maximum or Minimum Value

  16. Find the Maximum or Minimum Value

  17. Homework: Textbook pg. 61-63 # 9, 29, 41, 56

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